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Properties

Label 16.0.216...625.1
Degree $16$
Signature $[0, 8]$
Discriminant $2.166\times 10^{23}$
Root discriminant \(28.74\)
Ramified primes $5,29,941$
Class number $2$ (GRH)
Class group [2] (GRH)
Galois group $C_2^6:D_4$ (as 16T969)

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Show commands: Magma / Oscar / Pari/GP / SageMath

Normalized defining polynomial

Copy content comment:Define the number field
 
Copy content sage:x = polygen(QQ); K.<a> = NumberField(x^16 - 8*x^15 + 34*x^14 - 98*x^13 + 246*x^12 - 566*x^11 + 1142*x^10 - 1904*x^9 + 2832*x^8 - 3842*x^7 + 4638*x^6 - 4622*x^5 + 4216*x^4 - 3314*x^3 + 1646*x^2 - 401*x + 41)
 
Copy content gp:K = bnfinit(y^16 - 8*y^15 + 34*y^14 - 98*y^13 + 246*y^12 - 566*y^11 + 1142*y^10 - 1904*y^9 + 2832*y^8 - 3842*y^7 + 4638*y^6 - 4622*y^5 + 4216*y^4 - 3314*y^3 + 1646*y^2 - 401*y + 41, 1)
 
Copy content magma:R<x> := PolynomialRing(Rationals()); K<a> := NumberField(x^16 - 8*x^15 + 34*x^14 - 98*x^13 + 246*x^12 - 566*x^11 + 1142*x^10 - 1904*x^9 + 2832*x^8 - 3842*x^7 + 4638*x^6 - 4622*x^5 + 4216*x^4 - 3314*x^3 + 1646*x^2 - 401*x + 41);
 
Copy content oscar:Qx, x = polynomial_ring(QQ); K, a = number_field(x^16 - 8*x^15 + 34*x^14 - 98*x^13 + 246*x^12 - 566*x^11 + 1142*x^10 - 1904*x^9 + 2832*x^8 - 3842*x^7 + 4638*x^6 - 4622*x^5 + 4216*x^4 - 3314*x^3 + 1646*x^2 - 401*x + 41)
 

\( x^{16} - 8 x^{15} + 34 x^{14} - 98 x^{13} + 246 x^{12} - 566 x^{11} + 1142 x^{10} - 1904 x^{9} + \cdots + 41 \) Copy content Toggle raw display

Copy content comment:Defining polynomial
 
Copy content sage:K.defining_polynomial()
 
Copy content gp:K.pol
 
Copy content magma:DefiningPolynomial(K);
 
Copy content oscar:defining_polynomial(K)
 

Invariants

Degree:  $16$
Copy content comment:Degree over Q
 
Copy content sage:K.degree()
 
Copy content gp:poldegree(K.pol)
 
Copy content magma:Degree(K);
 
Copy content oscar:degree(K)
 
Signature:  $[0, 8]$
Copy content comment:Signature
 
Copy content sage:K.signature()
 
Copy content gp:K.sign
 
Copy content magma:Signature(K);
 
Copy content oscar:signature(K)
 
Discriminant:   \(216625969799691187890625\) \(\medspace = 5^{8}\cdot 29^{4}\cdot 941^{4}\) Copy content Toggle raw display
Copy content comment:Discriminant
 
Copy content sage:K.disc()
 
Copy content gp:K.disc
 
Copy content magma:OK := Integers(K); Discriminant(OK);
 
Copy content oscar:OK = ring_of_integers(K); discriminant(OK)
 
Root discriminant:  \(28.74\)
Copy content sage:(K.disc().abs())^(1./K.degree())
 
Copy content gp:abs(K.disc)^(1/poldegree(K.pol))
 
Copy content magma:Abs(Discriminant(OK))^(1/Degree(K));
 
Copy content oscar:(1.0 * dK)^(1/degree(K))
 
Galois root discriminant:  $5^{1/2}29^{1/2}941^{1/2}\approx 369.3846233940985$
Ramified primes:   \(5\), \(29\), \(941\) Copy content Toggle raw display
Copy content comment:Ramified primes
 
Copy content sage:K.disc().support()
 
Copy content gp:factor(abs(K.disc))[,1]~
 
Copy content magma:PrimeDivisors(Discriminant(OK));
 
Copy content oscar:prime_divisors(discriminant((OK)))
 
Discriminant root field:  \(\Q\)
$\Aut(K/\Q)$:   $C_2^2$
Copy content comment:Autmorphisms
 
Copy content sage:K.automorphisms()
 
Copy content magma:Automorphisms(K);
 
Copy content oscar:automorphisms(K)
 
This field is not Galois over $\Q$.
This is a CM field.
Reflex fields:  unavailable$^{128}$

Integral basis (with respect to field generator \(a\))

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $\frac{1}{5}a^{8}+\frac{1}{5}a^{7}-\frac{1}{5}a^{6}+\frac{2}{5}a^{5}-\frac{2}{5}a^{4}+\frac{1}{5}a^{3}+\frac{1}{5}a^{2}+\frac{2}{5}a+\frac{1}{5}$, $\frac{1}{5}a^{9}-\frac{2}{5}a^{7}-\frac{2}{5}a^{6}+\frac{1}{5}a^{5}-\frac{2}{5}a^{4}+\frac{1}{5}a^{2}-\frac{1}{5}a-\frac{1}{5}$, $\frac{1}{5}a^{10}-\frac{1}{5}a^{6}+\frac{2}{5}a^{5}+\frac{1}{5}a^{4}-\frac{2}{5}a^{3}+\frac{1}{5}a^{2}-\frac{2}{5}a+\frac{2}{5}$, $\frac{1}{5}a^{11}-\frac{1}{5}a^{7}+\frac{2}{5}a^{6}+\frac{1}{5}a^{5}-\frac{2}{5}a^{4}+\frac{1}{5}a^{3}-\frac{2}{5}a^{2}+\frac{2}{5}a$, $\frac{1}{5}a^{12}-\frac{2}{5}a^{7}-\frac{1}{5}a^{4}-\frac{1}{5}a^{3}-\frac{2}{5}a^{2}+\frac{2}{5}a+\frac{1}{5}$, $\frac{1}{5}a^{13}+\frac{2}{5}a^{7}-\frac{2}{5}a^{6}-\frac{2}{5}a^{5}-\frac{1}{5}a^{2}+\frac{2}{5}$, $\frac{1}{1987435}a^{14}-\frac{7}{1987435}a^{13}-\frac{172453}{1987435}a^{12}-\frac{157652}{1987435}a^{11}+\frac{186337}{1987435}a^{10}-\frac{82939}{1987435}a^{9}+\frac{118802}{1987435}a^{8}+\frac{665}{4789}a^{7}+\frac{162184}{1987435}a^{6}-\frac{941408}{1987435}a^{5}-\frac{887978}{1987435}a^{4}+\frac{912201}{1987435}a^{3}-\frac{145294}{397487}a^{2}-\frac{674028}{1987435}a+\frac{648721}{1987435}$, $\frac{1}{1393191935}a^{15}+\frac{343}{1393191935}a^{14}-\frac{121408438}{1393191935}a^{13}+\frac{32098269}{1393191935}a^{12}+\frac{73396438}{1393191935}a^{11}-\frac{58085959}{1393191935}a^{10}+\frac{127302543}{1393191935}a^{9}+\frac{118571666}{1393191935}a^{8}-\frac{24531878}{278638387}a^{7}+\frac{630986681}{1393191935}a^{6}-\frac{313686324}{1393191935}a^{5}+\frac{675490174}{1393191935}a^{4}-\frac{598458629}{1393191935}a^{3}+\frac{70166332}{278638387}a^{2}-\frac{350532309}{1393191935}a+\frac{144772541}{1393191935}$ Copy content Toggle raw display

Copy content comment:Integral basis
 
Copy content sage:K.integral_basis()
 
Copy content gp:K.zk
 
Copy content magma:IntegralBasis(K);
 
Copy content oscar:basis(OK)
 

Monogenic:  Not computed
Index:  $1$
Inessential primes:  None

Class group and class number

Ideal class group:  $C_{2}$, which has order $2$ (assuming GRH)
Copy content comment:Class group
 
Copy content sage:K.class_group().invariants()
 
Copy content gp:K.clgp
 
Copy content magma:ClassGroup(K);
 
Copy content oscar:class_group(K)
 
Narrow class group:  $C_{2}$, which has order $2$ (assuming GRH)
Copy content comment:Narrow class group
 
Copy content sage:K.narrow_class_group().invariants()
 
Copy content gp:bnfnarrow(K)
 
Copy content magma:NarrowClassGroup(K);
 
Relative class number:   $2$ (assuming GRH)

Unit group

Copy content comment:Unit group
 
Copy content sage:UK = K.unit_group()
 
Copy content magma:UK, fUK := UnitGroup(K);
 
Copy content oscar:UK, fUK = unit_group(OK)
 
Rank:  $7$
Copy content comment:Unit rank
 
Copy content sage:UK.rank()
 
Copy content gp:K.fu
 
Copy content magma:UnitRank(K);
 
Copy content oscar:rank(UK)
 
Torsion generator:   \( -1 \)  (order $2$) Copy content Toggle raw display
Copy content comment:Generator for roots of unity
 
Copy content sage:UK.torsion_generator()
 
Copy content gp:K.tu[2]
 
Copy content magma:K!f(TU.1) where TU,f is TorsionUnitGroup(K);
 
Copy content oscar:torsion_units_generator(OK)
 
Fundamental units:   $\frac{1498}{1987435}a^{14}-\frac{10486}{1987435}a^{13}+\frac{31956}{1987435}a^{12}-\frac{55418}{1987435}a^{11}+\frac{96952}{1987435}a^{10}-\frac{226678}{1987435}a^{9}+\frac{288707}{1987435}a^{8}+\frac{58}{4789}a^{7}-\frac{310412}{1987435}a^{6}+\frac{54692}{1987435}a^{5}-\frac{597029}{1987435}a^{4}+\frac{301348}{397487}a^{3}-\frac{225023}{397487}a^{2}+\frac{320523}{1987435}a-\frac{3251553}{1987435}$, $\frac{1718410}{278638387}a^{15}-\frac{63347516}{1393191935}a^{14}+\frac{251188021}{1393191935}a^{13}-\frac{134609171}{278638387}a^{12}+\frac{19770858}{16785445}a^{11}-\frac{3696256809}{1393191935}a^{10}+\frac{1438970328}{278638387}a^{9}-\frac{11217691404}{1393191935}a^{8}+\frac{16102264633}{1393191935}a^{7}-\frac{21291139961}{1393191935}a^{6}+\frac{4974150347}{278638387}a^{5}-\frac{22821320293}{1393191935}a^{4}+\frac{21276553441}{1393191935}a^{3}-\frac{3204580040}{278638387}a^{2}+\frac{981021967}{278638387}a-\frac{1660279583}{1393191935}$, $\frac{1718410}{278638387}a^{15}-\frac{63347516}{1393191935}a^{14}+\frac{251188021}{1393191935}a^{13}-\frac{134609171}{278638387}a^{12}+\frac{19770858}{16785445}a^{11}-\frac{3696256809}{1393191935}a^{10}+\frac{1438970328}{278638387}a^{9}-\frac{11217691404}{1393191935}a^{8}+\frac{16102264633}{1393191935}a^{7}-\frac{21291139961}{1393191935}a^{6}+\frac{4974150347}{278638387}a^{5}-\frac{22821320293}{1393191935}a^{4}+\frac{21276553441}{1393191935}a^{3}-\frac{3204580040}{278638387}a^{2}+\frac{981021967}{278638387}a-\frac{267087648}{1393191935}$, $\frac{86319702}{1393191935}a^{15}-\frac{645779857}{1393191935}a^{14}+\frac{2590350234}{1393191935}a^{13}-\frac{7048768976}{1393191935}a^{12}+\frac{17318987137}{1393191935}a^{11}-\frac{39193323983}{1393191935}a^{10}+\frac{76604275167}{1393191935}a^{9}-\frac{121036354621}{1393191935}a^{8}+\frac{174888040294}{1393191935}a^{7}-\frac{46144071638}{278638387}a^{6}+\frac{53319756007}{278638387}a^{5}-\frac{244002735208}{1393191935}a^{4}+\frac{219092215868}{1393191935}a^{3}-\frac{31509226914}{278638387}a^{2}+\frac{9480800713}{278638387}a-\frac{1091801582}{278638387}$, $\frac{32412602}{1393191935}a^{15}-\frac{241216536}{1393191935}a^{14}+\frac{192360543}{278638387}a^{13}-\frac{2596219814}{1393191935}a^{12}+\frac{1269837369}{278638387}a^{11}-\frac{14336591234}{1393191935}a^{10}+\frac{27940032162}{1393191935}a^{9}-\frac{43831174452}{1393191935}a^{8}+\frac{63117919924}{1393191935}a^{7}-\frac{83406743149}{1393191935}a^{6}+\frac{96835895678}{1393191935}a^{5}-\frac{88789855356}{1393191935}a^{4}+\frac{81443970372}{1393191935}a^{3}-\frac{12001118919}{278638387}a^{2}+\frac{18218293353}{1393191935}a-\frac{907991556}{1393191935}$, $\frac{12499830}{278638387}a^{15}-\frac{465290499}{1393191935}a^{14}+\frac{1861393174}{1393191935}a^{13}-\frac{5059280417}{1393191935}a^{12}+\frac{12451344664}{1393191935}a^{11}-\frac{28182883289}{1393191935}a^{10}+\frac{55032907962}{1393191935}a^{9}-\frac{86967362841}{1393191935}a^{8}+\frac{126003081579}{1393191935}a^{7}-\frac{166322289889}{1393191935}a^{6}+\frac{191825736429}{1393191935}a^{5}-\frac{175977058163}{1393191935}a^{4}+\frac{31696476483}{278638387}a^{3}-\frac{113781565438}{1393191935}a^{2}+\frac{34198373776}{1393191935}a-\frac{4365338617}{1393191935}$, $\frac{15936650}{278638387}a^{15}-\frac{594171249}{1393191935}a^{14}+\frac{2379069242}{1393191935}a^{13}-\frac{6469483484}{1393191935}a^{12}+\frac{15919074896}{1393191935}a^{11}-\frac{36043486853}{1393191935}a^{10}+\frac{14084968011}{278638387}a^{9}-\frac{22265981502}{278638387}a^{8}+\frac{161321215907}{1393191935}a^{7}-\frac{213144605464}{1393191935}a^{6}+\frac{246212015427}{1393191935}a^{5}-\frac{225924780192}{1393191935}a^{4}+\frac{204222663608}{1393191935}a^{3}-\frac{147322169826}{1393191935}a^{2}+\frac{44361211868}{1393191935}a-\frac{7616313018}{1393191935}$ Copy content Toggle raw display (assuming GRH)
Copy content comment:Fundamental units
 
Copy content sage:UK.fundamental_units()
 
Copy content gp:K.fu
 
Copy content magma:[K|fUK(g): g in Generators(UK)];
 
Copy content oscar:[K(fUK(a)) for a in gens(UK)]
 
Regulator:  \( 36913.3751226 \) (assuming GRH)
Copy content comment:Regulator
 
Copy content sage:K.regulator()
 
Copy content gp:K.reg
 
Copy content magma:Regulator(K);
 
Copy content oscar:regulator(K)
 

Class number formula

\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr \approx\mathstrut &\frac{2^{0}\cdot(2\pi)^{8}\cdot 36913.3751226 \cdot 2}{2\cdot\sqrt{216625969799691187890625}}\cr\approx \mathstrut & 0.192649303399 \end{aligned}\] (assuming GRH)

Copy content comment:Analytic class number formula
 
Copy content sage:# self-contained SageMath code snippet to compute the analytic class number formula x = polygen(QQ); K.<a> = NumberField(x^16 - 8*x^15 + 34*x^14 - 98*x^13 + 246*x^12 - 566*x^11 + 1142*x^10 - 1904*x^9 + 2832*x^8 - 3842*x^7 + 4638*x^6 - 4622*x^5 + 4216*x^4 - 3314*x^3 + 1646*x^2 - 401*x + 41) DK = K.disc(); r1,r2 = K.signature(); RK = K.regulator(); RR = RK.parent() hK = K.class_number(); wK = K.unit_group().torsion_generator().order(); 2^r1 * (2*RR(pi))^r2 * RK * hK / (wK * RR(sqrt(abs(DK))))
 
Copy content gp:\\ self-contained Pari/GP code snippet to compute the analytic class number formula K = bnfinit(x^16 - 8*x^15 + 34*x^14 - 98*x^13 + 246*x^12 - 566*x^11 + 1142*x^10 - 1904*x^9 + 2832*x^8 - 3842*x^7 + 4638*x^6 - 4622*x^5 + 4216*x^4 - 3314*x^3 + 1646*x^2 - 401*x + 41, 1); [polcoeff (lfunrootres (lfuncreate (K))[1][1][2], -1), 2^K.r1 * (2*Pi)^K.r2 * K.reg * K.no / (K.tu[1] * sqrt (abs (K.disc)))]
 
Copy content magma:/* self-contained Magma code snippet to compute the analytic class number formula */ Qx<x> := PolynomialRing(Rationals()); K<a> := NumberField(x^16 - 8*x^15 + 34*x^14 - 98*x^13 + 246*x^12 - 566*x^11 + 1142*x^10 - 1904*x^9 + 2832*x^8 - 3842*x^7 + 4638*x^6 - 4622*x^5 + 4216*x^4 - 3314*x^3 + 1646*x^2 - 401*x + 41); OK := Integers(K); DK := Discriminant(OK); UK, fUK := UnitGroup(OK); clK, fclK := ClassGroup(OK); r1,r2 := Signature(K); RK := Regulator(K); RR := Parent(RK); hK := #clK; wK := #TorsionSubgroup(UK); 2^r1 * (2*Pi(RR))^r2 * RK * hK / (wK * Sqrt(RR!Abs(DK)));
 
Copy content oscar:# self-contained Oscar code snippet to compute the analytic class number formula Qx, x = PolynomialRing(QQ); K, a = NumberField(x^16 - 8*x^15 + 34*x^14 - 98*x^13 + 246*x^12 - 566*x^11 + 1142*x^10 - 1904*x^9 + 2832*x^8 - 3842*x^7 + 4638*x^6 - 4622*x^5 + 4216*x^4 - 3314*x^3 + 1646*x^2 - 401*x + 41); OK = ring_of_integers(K); DK = discriminant(OK); UK, fUK = unit_group(OK); clK, fclK = class_group(OK); r1,r2 = signature(K); RK = regulator(K); RR = parent(RK); hK = order(clK); wK = torsion_units_order(K); 2^r1 * (2*pi)^r2 * RK * hK / (wK * sqrt(RR(abs(DK))))
 

Galois group

$C_2^6:D_4$ (as 16T969):

Copy content comment:Galois group
 
Copy content sage:K.galois_group(type='pari')
 
Copy content gp:polgalois(K.pol)
 
Copy content magma:G = GaloisGroup(K);
 
Copy content oscar:G, Gtx = galois_group(K); G, transitive_group_identification(G)
 
A solvable group of order 512
The 44 conjugacy class representatives for $C_2^6:D_4$
Character table for $C_2^6:D_4$

Intermediate fields

\(\Q(\sqrt{5}) \), 4.4.23525.1, 8.0.16049343125.1, 8.8.16049343125.1, 8.0.465430950625.2

Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.

Copy content comment:Intermediate fields
 
Copy content sage:K.subfields()[1:-1]
 
Copy content gp:L = nfsubfields(K); L[2..length(b)]
 
Copy content magma:L := Subfields(K); L[2..#L];
 
Copy content oscar:subfields(K)[2:end-1]
 

Sibling fields

Degree 16 siblings: data not computed
Degree 32 siblings: data not computed
Minimal sibling: This field is its own minimal sibling

Frobenius cycle types

$p$ $2$ $3$ $5$ $7$ $11$ $13$ $17$ $19$ $23$ $29$ $31$ $37$ $41$ $43$ $47$ $53$ $59$
Cycle type ${\href{/padicField/2.8.0.1}{8} }^{2}$ ${\href{/padicField/3.8.0.1}{8} }^{2}$ R ${\href{/padicField/7.4.0.1}{4} }^{4}$ ${\href{/padicField/11.4.0.1}{4} }^{2}{,}\,{\href{/padicField/11.2.0.1}{2} }^{4}$ ${\href{/padicField/13.4.0.1}{4} }^{4}$ ${\href{/padicField/17.8.0.1}{8} }^{2}$ ${\href{/padicField/19.4.0.1}{4} }^{2}{,}\,{\href{/padicField/19.2.0.1}{2} }^{4}$ ${\href{/padicField/23.4.0.1}{4} }^{4}$ R ${\href{/padicField/31.4.0.1}{4} }^{2}{,}\,{\href{/padicField/31.2.0.1}{2} }^{4}$ ${\href{/padicField/37.4.0.1}{4} }^{4}$ ${\href{/padicField/41.2.0.1}{2} }^{6}{,}\,{\href{/padicField/41.1.0.1}{1} }^{4}$ ${\href{/padicField/43.4.0.1}{4} }^{4}$ ${\href{/padicField/47.4.0.1}{4} }^{2}{,}\,{\href{/padicField/47.2.0.1}{2} }^{4}$ ${\href{/padicField/53.4.0.1}{4} }^{4}$ ${\href{/padicField/59.4.0.1}{4} }^{2}{,}\,{\href{/padicField/59.2.0.1}{2} }^{4}$

In the table, R denotes a ramified prime. Cycle lengths which are repeated in a cycle type are indicated by exponents.

Copy content comment:Frobenius cycle types
 
Copy content sage:# to obtain a list of [e_i,f_i] for the factorization of the ideal pO_K for p=7 in Sage: p = 7; [(e, pr.norm().valuation(p)) for pr,e in K.factor(p)]
 
Copy content gp:\\ to obtain a list of [e_i,f_i] for the factorization of the ideal pO_K for p=7 in Pari: p = 7; pfac = idealprimedec(K, p); vector(length(pfac), j, [pfac[j][3], pfac[j][4]])
 
Copy content magma:// to obtain a list of [e_i,f_i] for the factorization of the ideal pO_K for p=7 in Magma: p := 7; [<pr[2], Valuation(Norm(pr[1]), p)> : pr in Factorization(p*Integers(K))];
 
Copy content oscar:# to obtain a list of [e_i,f_i] for the factorization of the ideal pO_K for p=7 in Oscar: p = 7; pfac = factor(ideal(ring_of_integers(K), p)); [(e, valuation(norm(pr),p)) for (pr,e) in pfac]
 

Local algebras for ramified primes

$p$LabelPolynomial $e$ $f$ $c$ Galois group Slope content
\(5\) Copy content Toggle raw display 5.2.2.2a1.2$x^{4} + 8 x^{3} + 20 x^{2} + 16 x + 9$$2$$2$$2$$C_2^2$$$[\ ]_{2}^{2}$$
5.2.2.2a1.2$x^{4} + 8 x^{3} + 20 x^{2} + 16 x + 9$$2$$2$$2$$C_2^2$$$[\ ]_{2}^{2}$$
5.2.2.2a1.2$x^{4} + 8 x^{3} + 20 x^{2} + 16 x + 9$$2$$2$$2$$C_2^2$$$[\ ]_{2}^{2}$$
5.2.2.2a1.2$x^{4} + 8 x^{3} + 20 x^{2} + 16 x + 9$$2$$2$$2$$C_2^2$$$[\ ]_{2}^{2}$$
\(29\) Copy content Toggle raw display 29.1.2.1a1.2$x^{2} + 58$$2$$1$$1$$C_2$$$[\ ]_{2}$$
29.2.1.0a1.1$x^{2} + 24 x + 2$$1$$2$$0$$C_2$$$[\ ]^{2}$$
29.1.2.1a1.1$x^{2} + 29$$2$$1$$1$$C_2$$$[\ ]_{2}$$
29.1.2.1a1.1$x^{2} + 29$$2$$1$$1$$C_2$$$[\ ]_{2}$$
29.2.1.0a1.1$x^{2} + 24 x + 2$$1$$2$$0$$C_2$$$[\ ]^{2}$$
29.1.2.1a1.2$x^{2} + 58$$2$$1$$1$$C_2$$$[\ ]_{2}$$
29.2.1.0a1.1$x^{2} + 24 x + 2$$1$$2$$0$$C_2$$$[\ ]^{2}$$
29.2.1.0a1.1$x^{2} + 24 x + 2$$1$$2$$0$$C_2$$$[\ ]^{2}$$
\(941\) Copy content Toggle raw display Deg $2$$1$$2$$0$$C_2$$$[\ ]^{2}$$
Deg $2$$1$$2$$0$$C_2$$$[\ ]^{2}$$
Deg $2$$1$$2$$0$$C_2$$$[\ ]^{2}$$
Deg $2$$1$$2$$0$$C_2$$$[\ ]^{2}$$
Deg $4$$2$$2$$2$
Deg $4$$2$$2$$2$

Spectrum of ring of integers

(0)(0)(2)(3)(5)(7)(11)(13)(17)(19)(23)(29)(31)(37)(41)(43)(47)(53)(59)